Physics · Mechanical Properties Of Fluids · NEET
| Cross-section area (A) | Large | Small |
| Fluid speed (v) | Slow | Fast |
| Pressure (P) | High | Low |
| Volume flow rate (A v) | Same | Same |
Faster in the NARROW part. The same amount of water must pass every second (nothing is stored or lost). So through a small area the water must speed up. This is the equation of continuity: A times v = constant. Small A means big v. In the wide part A is big, so v is small and the water moves slowly.
Think of the total energy of the fluid. Bernoulli says for a horizontal pipe: P + (1/2) rho v squared = constant. This is energy per unit volume. It has two parts: the pressure part (P) and the motion part ((1/2) rho v squared). Their sum is fixed. In the narrow part the fluid speeds up, so the motion part grows. To keep the sum the same, the pressure part must shrink. So fast fluid has low pressure.
The pressure difference itself. Because pressure is higher behind (in the wide part) and lower ahead (in the narrow part), there is a net forward push on the fluid as it enters the narrow section. That net force does work on the fluid and increases its kinetic energy. So the pressure drop is not magic; it is exactly what accelerates the fluid.
The simple rule 'fast = low pressure' is cleanest for a horizontal pipe, because then height does not change and the rho g h term stays the same. If the pipe also goes up or down, you must keep the full Bernoulli equation P + (1/2) rho v squared + rho g h = constant and account for the height change too.
Less pressure means less outward push per unit area on the pipe wall in the narrow part. Students mix up 'more water rushing through' with 'more pressure'. The flow rate (volume per second) is the SAME everywhere in the pipe, but the pressure is lower where it is narrow and fast.
The venturi-meter works on:
Water flows in streamline motion through a horizontal pipe of circular cross-section. The pressure difference of water between P and Q is 15 N/m squared. The areas of cross-section at P and Q are 40 cm squared and 20 cm squared respectively. The rate of flow of water through the pipe (in cm cubed per second) is: [density of water = 1000 kg/m cubed]
Try the real previous-year questions from this chapter — each with the answer and a full solution.
In the WIDE part, where the fluid is slow. The narrow part has the lowest pressure because the fluid there is fastest.
Two together: continuity (A_1 v_1 = A_2 v_2) gives you the speeds, and Bernoulli for a horizontal pipe (P_1 + (1/2) rho v_1 squared = P_2 + (1/2) rho v_2 squared) links speed to pressure.
Yes. The volume of water passing per second (A times v) is the same everywhere in the pipe. Only the speed and the pressure change; the flow rate stays constant.
The rule 'fast means low pressure' still holds. Density rho only changes how big the pressure drop is: a denser fluid gives a larger pressure drop for the same speed change, because the (1/2) rho v squared term is bigger.
